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Graham McVicker edited Correcting read depth and GC.tex
almost 10 years ago
Commit id: f5cd8e8d2740fd965bf01f8549c9ca5e0577fd96
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\subsubsection{Fitting adjustment coefficients}
For each target region, $j$, we count the total number of
reads, reads across individuals, $v_j = \sum_i x_{ij}$, and calculate the GC content, $w_j$. Then, for each individual $i$, we find maximum likelihood estimates of the coefficients $a_{0i}, a_{1i}, \ldots, b_{4i}$ that define the adjusted total read depth $T^{*}_{i,j}$, given the observed read counts and GC content:
\[
\textrm{L}\left(a_{0i}, a_{1i}, \ldots, b_{4i} \left| D_i \right. \right ) = \prod_j \Pr_{\mathrm{Pois}} \left(X_{ij} = x_{ij} \left| T^{*}_{ij} \right. \right)\\